We just launched our startup with a designer helping us pro bono to spruce up the design of it. He's asking for compensation now (which is fair) and is willing to trade in his service for equity. Just wondering if it's better to pay than to trade equity for the service.
Find a way to pay for it. Giving up equity is an option of last resort and should only be reserved for very rare people and circumstances. When your business becomes valuable you will be very happy that you're not sharing it with your first web designer.